Quantization of the null-surface formulation of general relativity

Abstract

We define and discuss various quantum operators that describe the geometry of spacetime in quantum general relativity. These are obtained by combining the null-surface formulation of general relativity, recently developed, with asymptotic quantization. One of the operators defined describes a ``fuzzy'' quantum light cone structure. Others, denoted ``spacetime-point operators,'' characterize geometrically defined physical points. We discuss the interpretation of these operators. This seems to suggest a picture of quantum spacetime as made of ``fuzzy'' physical points. We derive the commutation algebra of the quantum spacetime-point operators in the linearization around flat space.